Based on the pinch point method and a modification of the fast algorithm a new combined strategy is proposed for completing the synthesis of heat-exchange networks. To avoid the violation of minimum energy consumption and the assignment of overcomplicated structures, two new types of pinch situation (hidden and pseudo pinches) are distinguished and two new rules are suggested. The total allowable heat load, determined iteratively, assures minimum energy consumption. The minimum heat load, as an arbitrary parameter, limits the exchangers' size and thus avoids the synthesis of overparcelled countercurrent cascades (too many, small, exchangers).